Here is a solution to run regressions on all other columns but the first.
The formula is created with reformulate.

suppressPackageStartupMessages({
  library(magrittr)
  library(purrr)
})

# create the formula with 'value' as regressor,
# it will be the column name after pivoting to long format
fmla <- reformulate("value", response = names(df1)[1L] |> as.name())
# run the regressions
lm_fit_list <- df1 %>%
  tidyr::pivot_longer(-1L) %>%
  split(.$name) %>%
  map(\(df) lm(fmla, data = df))
  
# this gives some statistics
lm_smry_list <- lm_fit_list %>% map(summary)
lm_smry_list %>% map(coef)
#> $`Canada 2Y Bond Price`
#>                 Estimate  Std. Error    t value   Pr(>|t|)
#> (Intercept)  0.001736073 0.003667346  0.4733866 0.64162781
#> value       -0.025789455 0.011690588 -2.2060015 0.04061964
#> 
#> $`Global Price`
#>                 Estimate  Std. Error    t value   Pr(>|t|)
#> (Intercept) -0.001515084 0.003712875 -0.4080622 0.68804100
#> value        0.164831106 0.070018144  2.3541199 0.03012634
#> 
#> $`Oil Price`
#>                 Estimate  Std. Error    t value  Pr(>|t|)
#> (Intercept) -0.001424249 0.004112478 -0.3463238 0.7331147
#> value        0.046411939 0.030404220  1.5264966 0.1442663
#> 
#> $`US - Canada Inflation`
#>                 Estimate  Std. Error    t value    Pr(>|t|)
#> (Intercept) 0.0001923356 0.003176245 0.06055441 0.952381362
#> value       0.0393945114 0.011325922 3.47826091 0.002683133

^{创建于2024-02-23，共reprex v2.0.2个}

Edit

在输出列表上运行summary之后，您可以从第二个列表(摘要)中提取所需的值.

suppressPackageStartupMessages({
  library(magrittr)
  library(purrr)
})

# create the formula with 'value' as regressor,
# it will be the column name after pivoting to long format
fmla <- reformulate("value", response = names(df1)[1L] |> as.name())
# run the regressions
lm_fit_list <- df1 %>%
  tidyr::pivot_longer(-1L) %>%
  split(.$name) %>%
  map(\(df) lm(fmla, data = df))
  
lm_smry_list <- lm_fit_list %>% map(summary)

stats <- lm_smry_list %>%
  map(coef) %>%
  map2(names(lm_smry_list), \(x, y) {
    data.frame(Variable = y) %>% cbind(x)
  }) %>% 
  list_rbind() 
row.names(stats) <- NULL
stats
#>                Variable      Estimate  Std. Error     t value    Pr(>|t|)
#> 1  Canada 2Y Bond Price  0.0017360725 0.003667346  0.47338661 0.641627809
#> 2  Canada 2Y Bond Price -0.0257894550 0.011690588 -2.20600149 0.040619640
#> 3          Global Price -0.0015150839 0.003712875 -0.40806217 0.688041004
#> 4          Global Price  0.1648311056 0.070018144  2.35411990 0.030126342
#> 5             Oil Price -0.0014242490 0.004112478 -0.34632381 0.733114717
#> 6             Oil Price  0.0464119390 0.030404220  1.52649664 0.144266337
#> 7 US - Canada Inflation  0.0001923356 0.003176245  0.06055441 0.952381362
#> 8 US - Canada Inflation  0.0393945114 0.011325922  3.47826091 0.002683133

^{创建于2024-02-23，共reprex v2.0.2个}